You work for a chicken soup manufacturer who believes she can introduce a differ

Question

You work for a chicken soup manufacturer who believes she can introduce a different dumpling(soy based) into her soup without affecting the incredible chicken flavor. To test this hypothesis, she produced 18 cans labeled Style "CHI" that contain the old flour based dumpling and 18 cans labeled Style "WHY" that contain the new soy based dumpling. She sends one can to each of 18 tasters and asks which they prefer, If her hypothesis is correct, we should expect 9 tasters to like CHI and 9 to like WHY. In the actual test, 11 preferred CHI, and the rest WHY. Calculate chi squared and the probability of getting a value this large or larger. Does the test indicate a significant difference between the two kinds of dumpling? Now calculate the probability exactly using the correct distribution model, and compare your results.

If you run another test with 400 cans, and 225 testers prefer CHI, has your hypothesis changed any? explain and justify.

Explanation / Answer

The chi square value would be :

Chi square = (11-9)^2/9 + (7-9)^2/9 = 4/9 + 4/9 = 8/9 = 0.8889

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df = 2

So P value = 0.6412

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Since the P value is very large it doesnot idicate a significance difference between the two kinds of dumpling.

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The correct test would be 2 proportions Z test

Proportion of people who liked chi P^ = 11/18 = 0.6111, whereas population proporiton P = 0.5

SE = square root of [0.5/0.5/18] = 0.1179

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Z = (0.6111 -0.5) / 0.1179 = 0.9423

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The P value for Z = 0.9423 is : 0.34604

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If in case the test was for 400 cans : and 225 prefer CHI , in that case the null hypothesis would remain the same that the proportion of people who prefer chi is 0.5

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